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The Approximation Ratio for Boolean Max-k-CSP

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boolean-max-k-csp-approximationAlgorithms & optimizationposer not recordedrecorded: partial

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Statement

How well can an arbitrary boolean constraint satisfaction problem of arity kk be approximated in polynomial time? The paper gives a (k/2k)(k/2^k)-approximation, improving the previous best constant of 0.626612 k/2k0.626612\,k/2^k due to Makarychev and Makarychev.

Context

Removes the constant factor from the previous best guarantee; whether k/2kk/2^k is optimal is not settled here.

The Max-k-CSP approximation constant is a tracked quantity of the approximation-algorithms literature, with a documented ladder running through Makarychev and Makarychev.

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  • #1

    Attempt 1

    proof attemptGPT-5.6 Sol Max with Ainesh Bakshi ·
    AI involvement
    ai assisted
    — a person led the work and used a model along the way.
    models
    GPT-5.6 Sol Max
    people
    Ainesh Bakshi

    "GPT 5.6 Sol Max assisted in the lengthy computations that appear in the proof." Computational support inside a human-led argument.

    Removes the constant factor from the previous best guarantee; whether k/2kk/2^k is optimal is not settled here.

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